50 
40-ton car and an S80-ton engine. The 40-ton car is the ship of the plains. 
Without it millions of acres now dotted by happy homes would have been 
unavailable for settlement. 
Up to this time but a small per cent. even of our educated people have 
been imbued with the spirit of the calculus and have appreciated its 
power. Indications point to a large expansion in the near future in the 
number of those who will cultivate it for the power that it will give. 
A popular German treatise upon this subject has recently been written 
expressly for chemists. 
The object of this treatise is easily deduced from a remark in it 
quoted from Jahn in his elements of electro-chemistry. He says: “Chem- 
ists must gradually accustom themselves to the thought that theoretical 
chemistry without the mastery of the elements of the higher analysis 
will remain for them a sealed book. For the chemist the differential or 
integral sign must cease to be a senseless hieroglyphic if he will avoid the 
danger of losing all comprehension of the theory of his subject, for it 
is fruitless labor to attempt to make clear in many weary pages what an 
equation says to the initiated in a single line.” 
By the higher analysis Guldberg and Waage have obtained formulae 
for studying the course and end of a chemical reaction. Neither in the 
application of analysis to chemistry are mathematical difficulties seriously 
in the way. The inner nature of the physical or chemical process is repre- 
sented as truly by the method and working of the higher analysis as an 
object is represented by its photograph. 
The power of the analysis in nature lies largely in its ability to deduce 
instantly from one set of laws another set equally important which at 
first sight do not seem to be closely related to it. For example, knowing 
the law of motion in space, we deduce velocity at any instant: knowing 
the chemical reaction as a whole, we deduce its intensity at any moment; 
from the weight of air and the law of gases we deduce its pressure at any 
height. 
To the chemist we must look for the solution of many problems, 
whether of theory or practice. Perhaps the greatest of these is the philo- 
sophie question of the ages—the nature of matter. If this question is ever 
definitely settled it will be by the chemist, with the aid of the calculus. 
The higher analysis in its services to mankind is not confined to the 
exact sciences. 
